Since we have the components of the position and the time for change, we could have differentiate the position with respect to time to calculate the components of Velocity and acceleration.

✅ Correct.

You are right. The velocity components are found by differentiating each position component ($x(t)$, $y(t)$, $z(t)$) with respect to time $t$. Similarly, the acceleration components are found by differentiating the velocity components with respect to time $t$. This is exactly what was done in the solution.